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Consider the degenerate electron gas in a metal as a mixture of two gases of spin-up and

spin-down electrons, respectively. when a small magnetic field B is applies, a few of the

electrons reverse their spins so as to maintain equality of the chemical potential in the two

mixed gases. For T = 0, find the magnetic susceptibility of the metal [tex] ( \frac{\partial M}{\partial B} )_N_,_V [/tex] ,

where M is the magnetization (magnetic moment per unit volume), N is the total number of electrons, and V is the volume. The magnetic moment of the electron is μB.

How do I use the information of chemical potential equality to solve this problem? I am thinking that since Gibbs, [tex] G_{up} = \mu n_{up} [/tex] and the same for spin down gas, the change, [tex] dG = \mu dn + n d \mu = \mu dn [/tex]. What next ?

spin-down electrons, respectively. when a small magnetic field B is applies, a few of the

electrons reverse their spins so as to maintain equality of the chemical potential in the two

mixed gases. For T = 0, find the magnetic susceptibility of the metal [tex] ( \frac{\partial M}{\partial B} )_N_,_V [/tex] ,

where M is the magnetization (magnetic moment per unit volume), N is the total number of electrons, and V is the volume. The magnetic moment of the electron is μB.

How do I use the information of chemical potential equality to solve this problem? I am thinking that since Gibbs, [tex] G_{up} = \mu n_{up} [/tex] and the same for spin down gas, the change, [tex] dG = \mu dn + n d \mu = \mu dn [/tex]. What next ?

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